Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic#curve with #period over the #circle's circumference and has #cusps whenever the point is in contact with the surface (the two sides of the curve are tangentially vertical at that point).
Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.
In a new paper, #researchers propose that the #dynamics of #rotatingblackholes is constrained by the principle of #gaugesymmetry, which suggests that some changes of parameters of a physical system would have no measurable effect.
"We observe that oxygen #dynamics in #chiral environments (in particular its transport) depend on nuclear #spin, suggesting future applications for controlled #isotope separation to be used, for instance, in #NMR. To demonstrate the mechanism behind our findings, we formulate theoretical models based on a #nuclear-spin-enhanced switch between #electronic spin states."
There’s been a lot of speculation around what Threads will be and what it means for Mastodon. We’ve put together some of the most common questions and our responses based on what was launched today:
@christianp@ColinTheMathmo
While I understand that getting a lot of users join #ActivityPub can be seen as an opportunity, it is known that #dynamics are strongly affected when in a systems you have huge actors and small actors. This is ... #maths! ;)
I found the article by @quokka (on whose instance I have my other account) very convincing, and I am all with the scicomm.xyz decision to choose a #prudentlyDefensive approach (block proactively and, if none of the anticipated problems materialise within time, consider removing the block) rather than #CautiouslyDefensive one (do nothing for now but take rapid action if-and-when something bad happens).
Does the fact that you have boosted this post from @Mastodon mean that mathstodon.xyz endorses this approach? Can you point me to a local discussion about this? Thanks.